The present invention generally relates to inference systems, and more particularly to an inference system having an artificial intelligence for processing uncertain knowledge.
Not all human knowledge is certain, and for this reason, it is essential that uncertain knowledge can be processed in machines. Such machines must have a function of processing fuzzy or vague statements which are subjected to digitization or number coding.
An inference (or reasoning) system generally gives questions to a user and obtains an information from answers entered by the user. This information used to infer a result is restricted every time an answer is entered by the user in response to a question given by the inference system, because candidates for an inferred result (hereinafter referred to as a conclusion) of the inference can be limited as more information is obtain ed from the answers entered by the user. Accordingly, the inference system eliminates the degree of fuzziness by successively giving questions to the user.
Such an inference system is employed in the so-called expert system, and the expert system usually uses a certainty factor (CF) in accordance with the MYCIN system for describing a degree of belief with respect to a statement which may not necessarily be certain. However, the certainty factor (CF) simply does not take into account the total coordination, and for this reason, there is a problem in that the inference may lead to a strange conclusion such as "believing 100% that a value of a variable is equal to X while at the same time believing 100% that the value of this variable is equal to Y which is different from X" and "believing 100% that it is impossible that a value of a variable is not Z while at the same time believing only 60% that the value of this variable is Z".
The Bayes probability and the fuzzy theory are well known as digitization techniques for fuzzy statements. However, probability cannot describe ignorance. For example, when there is no knowledge on the authenticity of a certain statement S, it is irrational no matter what value is set for a probability P(S) that the statement S is true. In other words, when a negation of the statement S is denoted by -S, an equation P(S)+P(-S)=1 must stand as long as probability is used. Hence, P(-S)&gt; P(S) stands when it is assumed that P(S)&lt;1/2, but one is ignorant on the authenticity of the statement S. Accordingly, one is also ignorant on the authenticity of the negation -S. But it is irrational that the probabilities P(S) and P(-S) differ even though one is ignorant on the authenticity of both the statement S and the negation -S.
On the other hand, in case the negation -S is a disjoint sum of statements S' and S" and one is ignorant on the statements S' and S", an equation P(S)+P(S')+P(S")=1 must stand when it is assumed that P(S)&gt;1/3. Hence, P(S)&gt;min{P(S'), P(S")} stands, and the irrationality also exists. Therefore, the probability P(S) must be 1/2 or greater and at the same time be 1/3 or less, and the irrationality exists no matter what value is set for the probability P(S).
The degree of ignorance can be described by the fuzzy theory. However, the processing of the fuzzy statements after being subjected to the digitization is extremely complex. For this reason, the fuzzy theory is suited for application in a high-speed processing such as a real-time control in which a feedback is obtained within a short time, but the reliability of the conclusion becomes poor when the fuzzy theory is applied to a processing having no feedback.
The Dempster-Shafer theory includes both the probability method and the fuzzy theory. Although the Dempster-Shafer theory is known, it is difficult to understand its general idea thereby making it difficult to apply the Dempster-Shafer theory to a knowledge processing system. In other words, it is difficult to set appropriate values, and the Dempster-Shafer theory is hardly used for processing fuzzy statements in actual practice.
Generally, the inference system gives the questions prepared beforehand to the user comprehensively. Accordingly, unnecessary questions and invalid questions are given and puts unnecessary burden on the user who must read and answer all of these questions.
Even in the case where all of the prepared questions are given, the user need not answer all of the questions if the inference system can process the fuzzy statements. In this case, the conclusion is obtained based on the answers to the questions the user elected to answer. However, there is still a burden on the user in that the user must read all of the prepared questions regardless of whether or not he elects to answer each question.
In the inference system which processes the fuzzy statements, the inference is made by converting data describing the possibility of a conclusion which will be obtained according to an answer to a question into Dempster-Shafer's basic probability assignment data, for example. As the conclusion which is obtained by the inference, there are a lower probability P.sub.* (A) which describes a degree of belief that the conclusion belongs to a set A, an upper probability P.sup.* (A) which describes a plausibility that the conclusion belongs to the set A, a degree of doubt D(A) which describes the degree of belief that the conclusion does not belong to the set A, a degree of ignorance U(A) which describes an ignorance to whether or not the conclusion belongs to the set A and the like. These values are displayed for the user as the final or intermediate conclusion. However, since these values are displayed to the user as numerical values, it is difficult for the user to make a total judgement from these values, and the conclusion is insufficiently informed to the user.